1. Rod says that he is thinking of a one variable polynomial expression that has the following characteristics: a. has a degree of 4 b. has three terms c. one of the terms has degree 1 d. one of the terms has a coefficient of -5 e. has a y-intercept at 10 What are two different polynomials that Rod could be thinking of? Are those the only possible answers? Please include an explanation or rationale with your response. [6 marks] 2. a question similar to #1 above, and provide a description of how a teacher could check that a student's response was correct. [3 marks] 3. Describe a function that has a. a domain of { | 2 10}, and b. a range of { | 5 10}. Your function does not need to be a polynomial or rational function, and it can be described algebraically, as a graph, or in another form. [4 marks] 4. Consider polynomial functions in the form () = + . Use at least three examples to investigate the relationship between a, n, and the constant finite differences. Explain the steps you took in your investigation and any conclusions you found. [6 marks] 5. Fully factor the following polynomials. Explain your thought process with your solution. a. () = 23 25 2 + 53 30 [3 marks] b. () = 3 + 3 4 [3 marks] 6. Sketch the graph of the function () = ( 4)( + 1) 2 ( 5). Explain your thinking. [4 marks] 7. Solve the equation 64 + = 53 + 22 . [4 marks] 8. Describe the transformations on the quartic function () = 14[3( 5)] 4 45. [2 marks] 9. Determine the values of m and n for () = 3 + 12 2 + 3 given that the remainder when dividing by ( + 3) is zero, and when divided by ( 2) the remainder is 85. [6 marks] 10. Use algebra to determine whether the function () = 22 3 19 is even, odd, or neither. [4 marks] 11. Graph the function () = 22 + 2 + 4 and its reciprocal on the same or separate axes. Explain your thinking. [5 marks] MHF4U Learning Activity 1.15 Unit 1 Assignment Copyright 2022 The Ontario Educational Communications Authority. All rights reserved. 2 TVO ILC 12. Sketch the graph of the function () = 2+3 5 . Describe its features and their relationship with the function. [5 marks] 13. Solve the inequality 2 3 2+5 97 . Include an interval chart in your solution. [4 marks] 14. Solve the inequality 8 3 2 + 1 17 8. Explain your solution in words. [5 marks] 15. Consider a box with dimensions 3 cm 5 cm 11 cm. If all of its dimensions are increased by x cm, what values of x will give a box with a volume between 300 cm3 and 900 cm3? [6 marks]